Problem: Solve for $x$ and $y$ using elimination. ${-4x+y = -33}$ ${3x-y = 23}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-4x+y = -33}\thinspace$ to find $y$ ${-4}{(10)}{ + y = -33}$ $-40+y = -33$ $-40{+40} + y = -33{+40}$ ${y = 7}$ You can also plug ${x = 10}$ into $\thinspace {3x-y = 23}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ - y = 23}$ ${y = 7}$